We have two responses, one from Penny and another from Stephen La Rocque.
Julie,
I like the way you have asked this question as it gives a direct way to translate the question from an english sentence to a mathematical sentence, an equation.
"what" is the unknown so give it a letter name. I'll call it x.
"percentage" is percent or per one hundred, in other words over 100.
"of" is multiplication. For example onethird of twelve is ^{1}/_{3} 12 = 4.
"is" is the verb and in an equation the verb is the equal sign.
Thus
What percentage of 120 is 24?
becomes
^{x}/_{100} 120 = 24
Solve for x.
Penny
Hi Julie. Percentages are ratios (fractions) where the denominator is always 100. This means
that when we ask what percentage one number is of another number, we are asking for the numerator of an equal sized fraction whose denominator is 100.
For example, if you asked "What percentage of 75 is 30?" Then we'd set up the fraction:
30 / 75 and try to turn it into something / 100.
Remember that with fractions, we can multiply (or divide) the numerator and the denominator by the same number without changing the value of the fraction.
In our example, we would divide the 30 by 15 (giving 2) and 75 by 15 (giving 5), so we know that 30 / 75 = 2 / 5. Now remember we are trying to make the bottom 100, so we need to multiply top and bottom by 20 because 5 x 20 = 100. So we also multiply the top by 20 and get 2 x 20 = 40. That means that 30 / 75 = 2 / 5 = 40 / 100 and since the 40 is on top of the 100, that is the percentage!
By the way, "percent" actually comes from "per cent" and if you look at the change in your pocket, you'll realize that cent refers to 100, because there are 100 cents in a dollar. So a percentage is the amount per hundred. That's an easy way to remember what to do.
With your question, start by writing the fraction 24 / 120 and now multiply and divide the top and bottom the same way to get 100 on the bottom.
Hope this helps!
Stephen La Rocque>
